Can we calculate the probability that Shirley McKie is telling the truth?

If someone is accused of lying in similar circumstances to Shirley McKie (not related to a pre-existing crime), I think that the likelihood that they are lying compared with the likelihood that they are telling the truth might be estimated as follows:

 

For any given area and time period estimate the ratio of:

 

The number of people who have their fingerprints checked during investigations who visit the crime scene and will lie about it and will leave a useable latent but leave no other evidence of their presence and are unseen by anybody but will not be charged with the original crime. This will be a small number and will be impossible to estimate.

 

to:

 

The number of misidentifications from all fingerprint activity in the area and time period that could lead to an allegation not related to the crime under investigation.  This will also be a small number and will be impossible to estimate.

 

This is at best a "balance of probabilities" situation.  Nobody should be accused of lying on the ratio of two small numbers that are impossible to estimate.  In a normal crime-led accusation (case 3) we are on much more solid ground because we would be comparing a big number (because the criminal visited the crime scene the probability of finding his or her latent is high), to a very small number (because we have minimised the risk of misidentification by limiting the investigation to only a few hundred latents).

 

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